Ternary linear codes and quadrics

For an [n, k, d](3) code C with gcd (d, 3) = 1, we define a map w(G) from Sigma = PG(k - 1, 3) to the set of weights of codewords of C through a generator matrix G. A t-flat Pi is Sigma called an (i, j)(t) flat if (i, j) = (vertical bar Pi boolean AND F(0)vertical bar, vertical bar Pi boolean AND F(1)vertical bar) , where F(0) = {P is an element of Sigma vertical bar w(G) (P) equivalent to 0 (mod3)}, F(1) - {P is an element of Sigma vertical bar w(G) (P) not equivalent to 0, d (mod3)}. We give geometric characterizations of (i, j)(t) flats, which involve quadrics. As an application to the optimal linear codes problem, we prove the non-existence of a [305, 6, 202](3)code, which is a new result.